Abstract
The stress ellipsoid is useful for visualizing the orientations and relative magnitudes of the principal stresses at a point, and for clarifying the relationship between stress vectors on individual planes and the stress tensor represented by the orientation and shape of the whole ellipsoid. But the stress ellipsoid is not very convenient for showing the relationship between the orientation of a plane and the magnitudes of the shearing and normal stresses upon it. For this we introduce a new kind of diagram called a Mohr diagram. Mohr diagrams are important because the normal and shear components of stress on a plane play a prominent role in theories of many planar structures, such as faults, joints, and deformation lamellae in crystals.
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Notes and References
Mohr diagrams for stress in two dimensions are discussed by Johnson (1970, pp. 205–208, pp. 339–345) and in three dimensions by Naidai (1950, pp. 96–99), Jaeger (1969, pp. 18–20), Jaeger and Cook (1969, pp. 27–30), and Mase (1970, pp. 55–56).
An alternative development of Equations 9.3 and 9.4 can be followed by reading Bombolakis (1968a) through his page 45.
The concepts of mean stress and deviatoric stress are explained by Bombolakis (1968a, pp. 47–49); the Mohr circle for stress is discussed on his pages 49–55. This treatment will be helpful to readers who want exposure to Mohr circles for compressive stress that plot to the left of the origin (i.e., where compressive stresses are taken as negative).
A comprehensive summary of graphical representations of the state of stress at a point, including the stress ellipsoid, Mohr circles, and other geometrical representations, is given by Durelli et al. (1958, pp. 63–80).
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© 1976 Springer-Verlag New York Inc.
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Means, W.D. (1976). Mohr Circle for Stress. In: Stress and Strain. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9371-9_9
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DOI: https://doi.org/10.1007/978-1-4613-9371-9_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-07556-3
Online ISBN: 978-1-4613-9371-9
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